Question

Find The length and breadth of a room with area 120m² and perimeter 44m

Answer 1

Let the length be a and the breadth be b

Given a x b = 120

2 (a + b) = 44

a + b = 22

b = 22 - a

a (22 - a) = 120

a² - 22 a + 120 = 0


a = 12 or a = 10

If a = 12, then b = 10

If a = 10 then b = 12

Answer 2

Answer:

Let the sides of our rectangle be “a” and “b”.

The perimeter of a triangle = sum of the lengths of its side = 2a + 2b.

Area of a rectangle = length * breadth

= ab.

Perimeter = 2a + 2b = 44. Which implies that,

a + b = 22.

Area = ab = 120.

And we know,

(a - b)^2 = (a + b)^2 - 4ab

From this if we calculate the value of a - b, we can figure out the value of “a” and “b”.

(a - b)^2 = (22)^2 - 4*120

= 484 - 480 = 4.

Which implies that,

a - b = 2, or a - b = - 2.

{ Doesn't really matter because I had not defined which one is length and breadth in “a” and “b” and so their values are interchangeable }

And we had found out before that,

a + b = 22, through our perimeter.

If we solve these two equations, we get,

a = 12, b = 10.

Hope this solution will help you ✨